here the justification for this incidental conception, which is indeed a somewhat
arbitrary one. We shall only mention that with its aid electromagnetic
phenomena can be theoretically represented much more satisfactorily than
without it, and this applies particularly to the transmission of electromagnetic
waves. The effects of gravitation also are regarded in an analogous manner.
The action of the earth on the stone takes place indirectly. The earth produces in
its surrounding a gravitational field, which acts on the stone and produces its
motion of fall. As we know from experience, the intensity of the action on a
body dimishes according to a quite definite law, as we proceed farther and
farther away from the earth. From our point of view this means : The law
governing the properties of the gravitational field in space must be a perfectly
definite one, in order correctly to represent the diminution of gravitational action
with the distance from operative bodies. It is something like this: The body (e.g.
the earth) produces a field in its immediate neighbourhood directly; the intensity
and direction of the field at points farther removed from the body are thence
determined by the law which governs the properties in space of the gravitational
fields themselves.
In contrast to electric and magnetic fields, the gravitational field exhibits a most
remarkable property, which is of fundamental importance for what follows.
Bodies which are moving under the sole influence of a gravitational field receive
an acceleration, which does not in the least depend either on the material or on
the physical state of the body. For instance, a piece of lead and a piece of wood
fall in exactly the same manner in a gravitational field (in vacuo), when they
start off from rest or with the same initial velocity. This law, which holds most
accurately, can be expressed in a different form in the light of the following
consideration.
According to Newton's law of motion, we have
(Force) = (inertial mass) x (acceleration),
where the "inertial mass" is a characteristic constant of the accelerated body. If
now gravitation is the cause of the acceleration, we then have
(Force) = (gravitational mass) x (intensity of the gravitational field),
where the "gravitational mass" is likewise a characteristic constant for the body.
From these two relations follows: